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Essential Travel, which claims to be the first British firm to adopt such a policy, said customers who have an accident and are proven to have been skiing without head protection face having their policy invalidated.

The move is part of an ongoing safety campaign by the insurer, “Use Your Head”, which was launched in 2010 following the death of Natasha Richardson a year earlier.

The actress died after sustaining a head injury during a skiing lesson at the Mont Tremblant resort in Canada. She was not wearing a helmet when she fell, and her death prompted a debate about ski safety, with some observers calling for head protection to become mandatory.

According to a recent survey by Essential Travel, around 77 per cent of British skiers now claim to wear a helmet on the slopes, up from 62 per cent in 2010.

“Whilst it is true that a helmet does not reduce all sports injury, it seriously reduces the risk of potentially fatal injuries,” said Stuart Bensusan of Essential Travel. “That alone warrants making wearing helmets compulsory, and we choose to completely support safety conscious skiers by rewarding them with reduced premiums and bonus discounts.”

A spokesman for the company admitted that while it may not always be able to prove whether or not a customer had been wearing a helmet, it would examine medical records and doctors’ notes for clues.

The Use Your Head campaign has the backing of the charity Headway, and several tour operators, including Ellis Brigham and Neilson, with several offering discounts on holidays if they book insurance through Essential Travel.

It is thought that other insurers may now follow suit by adopting similar policies.